Photoelectric endpoint detection

ABSTRACT

A method and apparatus useful for colorimetric titration utilizes an indicator which changes from one colored form to another at or near an endpoint, and an optical endpoint detection system which generates signals responsive to the relative concentrations of the different colored forms of the indicator. The endpoint is indicated when the ratio of the logarithms of the signals reaches a predetermined value.

United States Patent 1 Dahms 1 PHOTOELECTRIC ENDPOINT DETECTION [76] Inventor:

[22] Filed:

Harald Dahms, 22 Lakeview Rd., Ossining, N.Y. 10562 Dec. 21, 1970 [21] Appl. No.2 100,306

Related US. Application Data [63] Continuation-impart of Ser. No. 690,270, Dec. 13,

1967, Pat. No. 3,551,109.

..... ..23/230 R, 23/230 B, 23/253 R,

References Cited UNITED STATES PATENTS 1 Mar. 27, 1973 2,621,671 12/1952 Eckfeldt ..23/253 A 3,540,825 11/1970 Grojean 250/218 X 3,266,504 8/1966 Sundstrom ..23/253 R 3,275,533 9/1966 Boronkay 23/253 R 3,551,109 12/1970 Dahms 23/230 B 3,528,749 9/1970 Bowker ..356/206 R 3,551,350 12/1970 Dahms ..23/230 B 3,554,654 l/197l Paatzsch.... .....250/218 X 3,600,099 8/1971 Schoefiel ..356/206 Primary Examiner-Morris O. Wolk Assistant Examiner-Sidney Marantz Attorney--Griswold & Burdick, C. Kenneth Bjork and Maynard R. Johnson [57] ABSTRACT is indicated when the ratio of the logarithms of the signals reaches a predetermined value.

Brodkorb v.23/253 R Frenk ..250/218 9' Claims, 2 Drawing Figures 44 T m I" T ch /0 r /oe b/ta r Zo rfa/e I Re/a T 7 52 5 .swh ch fg g'j Re/oy T l -1 2 1 Vo r age Mer e/l Lo ar/Mm/c Me rer supp/y re/ay r af/omefer re/ag v- Z10 J\ r mofor' PHOTOELECTRIC ENDPOINT DETECTION CROSS-REFERENCE TO RELATED APPLICATION This is a continuation-in-part of my copending application, Ser. No. 690,270, filed Dec. 13, 1967, now U.S. Pat. No. 3,551,109.

SUMMARY OF THE INVENTION This invention is directed to titration of liquids and is particularly concerned with the detection of endpoints in colorimetric titrations. More particularly, the invention is concerned with automatic titration apparatus, comprising means for introducing a titrant ion into a liquid to be titrated, detection means for detecting the endpoint of the titration and means responsive to the detecting means for indicating the amount of titrant ion required to achieve the endpoint. One such device is described in my above-mentioned copending application, wherein a sample of blood serum is mixed with an acidic solution containing silver ions to precipitate a portion of the chloride and to drive off carbon dioxide. Titrant ions are introduced by electrolysis of the resulting liquid to produce additional silver ions (at an anode) and hydroxyl ions (at a cathode). The chloride end point is detected amperometrically, while the acidbase end point is detected by a pH electrode, and meter relays and clock timers are employed to indicate the amounts of the titrant ions required to achieve the endpoints. In a preferred embodiment, this invention is concerned with such a device wherein the endpoint of the acid-base titration is determined colorimetrically by means of a dual wavelength photodetector system and an indicator substance in the titration solution, rather than by a pH electrode.

In the device of the invention, the titration endpoint is detected by means of an indicator substance (which can indicate by a change of its light absorbing properties which side of a color change interval prevails in the titration solution) added to the titration solution; a light source which is provided to direct light through the titration solution, through a pair of filters to provide filtered light beams at two wave lengths or wave bands corresponding to the different absorbance characteristics of the different forms of the indicator on the opposite sides of the color change interval for the indicator, reaction and analysis employed, and to a photoelectric light detector or detectors for providing electrical signals responsive to the intensity of the filtered light beams; and a logarithmic ratiometer, which converts the signals provided by the light detectors to a logarithmic ratio signal, that is, a signal which corresponds to the logarithm of the ratio, or preferably the ratio of the logarithms of the initial signals. The endpoint of the titration is detected when the ratio of the logarithms of the two light-responsive signals (or logarithm of the ratios) reaches a predetermined value, which can be readily determined by calibration with standard solutions.

The indicator substance can be a known titration indicator of the type employed in conventional colorimetric titrations, such as those described in U.S. Pat. No. 3,481,707. Such indicators exist in different forms each having a characteristic color and light absorption properties on opposite sides of a color change interval which is indicative of the endpoint of the titration. Such indicators include the pH indicators, such as phenol red, phenolphthalein, m-cresolsulfonphthalein, bromcresol green, methyl violet 6B, nitramine or the like, and oxidation-reduction indicators such as nitroferroin, methylferroin, diphenylamine, naphthidine, eiroglaucin A or the like. The pH indicators have characteristic acid and base forms, and the oxidation-reduction indicators have characteristic oxidized and reduced forms depending upon pH or oxidation-reduction potential of the solution.

Each filter is selected to pass light which colorimetrically responds in intensity to the absorbance (and thus the concentration) of each of the two forms of the indicator, so that the photoelectric light detector means provides a pair of signals each of which similarly responds to the concentration of one form of the indicator, as in conventional colorimetric titration. The light detector signals, corresponding to the intensity of the filtered light beams, are also affected by such 'extraneous factors as the turbity of the titration solution, the amount of indicator present, and occurrence of side reactions in the titration solution, so that the unmodified signals alone do not provide the desired precision and accuracy of endpoint detection. In the present invention, the light detector signals are converted to a logarithmic ratio signal, which is preferably proportional to the ratio of the logarithms of the two filtered light beams, which greatly enhances the accuracy and precision of the endpoint detection and minimizes problems created by extraneous influences on the light intensity.

In the present invention, it is greatly preferred to employ a logarithmic ratiometer which converts the light detector signals to a logarithmic ratio signal proportional to the ratio of the logarithms of the intensities of two filtered light beams, rather than the logarithm of the ratio of intensities, as the fbrmer logarithmic ratio permits much greater accuracy and precision than the latter, and is much more independent of indicator concentration. Other advantages of the invention will be apparent on consideration of the following description and the drawings.

BRIEF DESCRIPTION OF THE VIEWS OF THE DRAWING FIG. 1 is a schematic diagram illustrating the device of the invention in a titrating apparatus of the type described in my aforesaid patent application.

FIG. 2 is a schematic diagram illustrating the logarithmic ratiometer of the device illustrated in FIG. 1.

DESCRIPTION OF PREFERRED EMBODIMENTS As illustrated in FIG. 1 the endpoint detection apparatus and method of the invention is employed with a chloride/bicarbonate determination apparatus as described more fully in my copending application, Ser. No. 690,270, filed Dec. 13, 1967. In FIG. 1, a liquid 12 to be titrated is contained in a transparent titration vessel 13. A silver anode 14, a cathode 16 (both connected to a constant current 39, which supplies a constant current to the anode and cathode); a pair of amperometric electrodes 17, 18 (connected to an electrical circuit comprising a voltage supply 41 and a meter relay 42 which supplies a constant voltage across these electrodes); a stirrer l9 (driven by a motor 51) and a bubbler 21 (connected to an air pump 52) are immersed in the liquid 12. The meter relay 42 is arranged to switch off the flow of current to a relay 43 which, in turn, acts to switch off the flow of current to a timer 44 having a direct readout (indicating chloride content). This circuitry is of the type described in the article by Cotlove and Nishi, Clinical Chemistry, 7, 285-291 (1961).

The titration vessel 13 is a transparent and adapted to permit uniform transmission of light therethrough as in conventional colorimeter cuvets. A lamp 201 provides light which is collimated by a collimating lens 202 and directed through vessel 13 and liquid 12 (as illustrated by broken lines 230), through a pair of filters 205, 206, which provide filtered beams 204, 207 of light to a pair of light detectors 215, 216, such as a pair of photocells. The light detectors 215, 216 are electrically connected to a logarithmic ratiometer 210, which is connected through a signal level detector, e.g., meter relay 47, to a relay 48 and timer 49 having a direct readout indicating bicarbonate content. Relays 43 and 48 are connected by time delay relays to switch 53, is also connected to the constant current supply 39, the lamp 201 and light detectors 215, 216 by conventional connections (not shown).

With the exception of the lamp 201, collimating lens 202, filters 205, 206, light detectors 215 and 216 and the logarithmic ratiometer 210, the apparatus is generally identical in construction and operation to that described in more detail in my copending application, Ser. No. 690,270, 270, filed Dec. 13, 1967, with meter relay 47 being connected to logarithmic ratiometer 210, rather than to a pH meter.

The logarithmic ratiometer 210, as illustrated in FIG. 2, comprises a pair of logarithmic amplifiers 211 and 212 each connected in series between a corresponding light detector 215, 216 and a ratiometer 213. The logarithmic amplifiers 211, 212 are conventional operational amplifiers which convert an input signal (from one of the photoelectric detectors) to an output signal proportional to the logarithm of the input signals. For convenience, the intensities of the filtered light beams 204, 207 measured by the detectors 215, 216 can be designated 1 and 1 The ratiometer 213 is also a conventional circuit for converting the input signals (corresponding to log I and log I to an output signal proportional to the ratio of the input signals (the output signal thus corresponding to log l /log I The ratiometer 213 can be, for example, a one quadrant multiplier/divider such as is described by Robert C. Dobkin in a technical bulletin of the National Semiconductor Corporation, Logarithmic Converters AN-30, November, 1969.

The input signals to the logarithmic amplifiers 211 and 212 (and thus the output signals from the light detectors 215 and 216) thus constitute measurements of the intensities l and 1 of filtered light beams 204, 207.

The output signals from the logarithmic amplifiers 211 and 212 thus correspond to log I and log 1 respectively. The ratiometer 213 provides an output signal proportional to the ratio of its two input signals from the logarithmic amplifiers 211 and 212 to provide an output signal corresponding to the ratio log l /log 1 The output of the ratiometer 213 is connected in series to a level detector, e.g meter relay 47"which is preset to be actuated when the output current corresponds to the preselected endpoint pH value. The endpoint pH value can be a pH value of 7.4, for example, which is a generally accepted endpoint in clinical titrations for determination of bicarbonate.

The endpoint pH need not coincide exactly with the equilibrium pH value of the indicator, and generally the two will not coincide. The endpoint pH value also the endpoint of the titration need not be precisely within the c0l0r-change interval for the indicator, so long as the color-change interval is sufficiently close to the endpoint (in pH value or oxidation-reduction potential or other basis of the titration) to be indicative of the endpoint. That is, the color-change interval of the indicator and the endpoint should be close enough to permit colorimetric measurement of both forms of the indicator at the endpoint.

For best results the endpoint pH value should fall within the pH range within which the indicator changes between its predominantly acid form and its predominantly basic form, i.e., the color-change interval of the indicator employed.

Once a given endpoint pH value is selected, an appropriate indicator can be selected from those having a pH range or pH interval which includes the endpoint, for example, by reference to standard tabulations of indicators such as the Merck Index, 8th Edition, pp. 1304-7, or Kolthoff and Laitenen, pH and Electro titrations, second Ed., Wiley, New York (1941) P. 29. Appropriate filters 205 and 206 can be selected to correspond to the absorbance maxima of the acid form and base form of the indicator. For bicarbonate titrations (having an endpoint pH value of about 7.4) phenol red is a preferred indicator, changing from a visible yellow color in the acid form to a visible red color in the base form over a pH range of 6.8 to 8.4. Suitable bandpass filters 205, 206 are selected so that filter 206 passes light having a wavelength of from about 430 to about 440 nanometers (corresponding to the acid form) and the other filter 205 passes light having a wavelength of from about 550 to about 560 nanometers (corresponding to the base form). Suitable filters are, for example, Wratten No. 98 in combination with No. 2A and Wratten No. 53 in combination with No. 15.

It is not critical which of the colorimetric filters 205, 206 measures the acid form of the indicator and which measures the base form, since reversing the filters 205, 206 merely changes the direction from which the predetermined value of the logarithmic ratio signal is approached. The same result is produced by reversing the direction of the titration, e.g., from titrating acid with an alkaline titrant to titration of an alkaline sample with an acid titrant. For a given logarithmic ratiometer 210 and a given meter relay 47, it is preferred that the filters 205, 206 be selected in relation to the desired direction of titration so that the logarithmic ratio output of the logarithmic ratiometer 210 approaches the endpoint value in the same direction in each titration (i.e., log l llog I uniformly either increases or decreases to the endpoint value). In a particularly preferred embodiment, the filters 205, 206 are selected so that the intensity I of filtered light beam 204 corresponds colorimetrically to the form of the indicator which predominates at the beginning of the titration,

thus providing a ratio log l llog l which increases during the titration until the endpoint value is reached. For example, the concentration C of the form of the indicator which predominates in the liquid at the beginning of the titration decreases during the titration, while the concentration C of the other form of the indicator increases as the endpoint is approached. By selecting the filters 205, 206 so that the intensity I of beam 204 responds to C and the intensity I of beam 207 responds to C the logarithmic ratio signal (log l,/log will increase during the titration. When the direction of the titration is to be reversed, the positions of filters 205, 206 can be reversed relative to their respective light detectors 215, 216 or an appropriate switch can be provided in the endpoint detection circuit to obtain an equivalent result. The provision of an increasing logarithmic ratio signal regardless of the direction of the titration simplifies the device by eliminating any necessity for the output voltage or current from the logarithmic ratiometer to pass through the predetermined endpoint value at the beginning of a titration.

in operation, the liquid 12 to be titrated, e.g., 0.1 milliliter of human blood serum, 4.0 milliliters of aqueous, chloride-free titration solution (2.l25 mM silver nitrate, 1.875 mM nitric acid and 0.1 molar potassium nitrate) is measured into the titration vessel 13, and a small amount, e.g., one or two drops, of phenol red indicator are added. The vessel 13 is placed in position in which the various electrodes of the device are immersed in the solution, as indicated in FIG. 1. The bubbler 21 and stirrer 19 are placed in operation and the circuit connecting the voltage supply 41 to the amperometric electrodes 17, 18 is closed; a small background current flows through the solution between these electrodes. In order to start the electrolysis, switch 53 is now thrown which starts the flow of electrolysis current through the solution generating silver ions at anode l4, and hydroxyl ions at the cathode 16. Switch 53 also starts timers 44 and 49, and activates lamp 201 and the light detectors 215, 216 and logarithmic ratiometer 210. The electrolysis proceeds until the endpoint of the titration of chloride with electrolytically generated silver ion at silver anode 14 is reached. At this point, an excess of silver ion occurs in the solution giving rise to an elevation of current flowing through the amperometric electrodes l7, l8 and also through meter-relay 42, which actuates relay 43, shutting off timer 44 and the voltage supply 41.

The electrolysis current is, however, not interrupted and continues generation of hydroxyl ions for titration of the remaining acid added in the titration solution.

As the titration proceeds toward the endpoint the concentration of the acid form of the phenol red indicator decreases while the concentration of the base form increases, and the two filtered light beams 204, 207 reaching the light detectors 215, 216 change intensity, i.e., the intensity l of the light beam 204 filtered by filter 206 (430-440 nanometers) to respond to the acid form of the indicator increases relative to the other beam's intensity I as the concentration of the acid form decreases, with a decrease in relative intensity 1 of the other beam 207 (filtered by filter 205, 550-560 nanometers) occuring as the concentration of the base form increases. In actual use, the absolute intensity of both beams may be decreasing due to increased turbity or the like and the relationship of concentration to intensity may or may not follow Beers Law without producing any adverse effect on the endpoint determination.

The base titration proceeds until the logarithmic ratiometer 210 indicates that the desired endpoint ratio of logarithms has been reached. At this time, the meter relay 47, which had been pre-set for the desired pH endpoint, actuates relay 48, which in turn stops timer 49, the electrolysis current, and the stirrer motor. The analysis is now completed and timers 44 and 49, indicating the chloride and the bicarbonate concentrations, respectively, can be read. After removal of the analysis solution, a brief rinse of the electrodes and vessel l3 and the re-setting of the timers, the apparatus is ready for the next analysis.

Since the optical endpoint detection apparatus of the invention detects the relative amounts of both forms of the indicator on either side of the endpoint, the absolute amount of indicator employed in a titration is not critical. Detection of the endpoint pH value from a predetermined value of the ratio of the logarithms of the signals also enhances the accuracy and precision of the titration, even in the presence of light fluctuations and changing turbidity in the titration vessel.

Alternatively the device can be readily modified to perform the bicarbonate titration alone, or to perform other titrations. Methods other than electrolysis can be employed for incorporating the titrant ion to attain the endpoint. The titration may be effected manually or with conventional automatic titrators controlled, in the same way as the electrolysis is controlled, by the endpoint-detecting light detectors and ratiometer previously described. The automatic titrator may be of the type in which a motor driven piston gradually forces a titrant liquid from a burette, and the motor of the automatic titrator may be connected to the detecting system in the same fashion as the constant current supply described previously. Digital readout may also be obtained by a conventional type of curcuit in which the motor of the timer (or of the burette piston) drives the movable contact of a potentiometer to continuously change its output voltage, which output voltage is fed to an operational amplifier, and the output voltage of the amplifier can be displayed at a digital voltmeter. Also, the photoelectric endpoint detection can be modified by conventional procedures. For example, the light transmitted through the liquid 12 can be passed through the filters before being directed through the liquid, or in lieu of the two photodetectors, a single photodetector can be employed with the two filters in a rotating filter wheel or chopper, so that the two light beams corresponding to the two forms of the indicator are presented sequentially, rather than simultaneously. In the latter case a synchronization signal can be provided to distinguish the different beams, with appropriate gating circuits and smoothing capacitors to separate the two signals before they are fed to the logarithmic ratiometer. In another modification, the meter relay 47 can be an adjustable level detector, i.e., it can be precalibrated to respond to a selected one of several different endpoints for different titrations, with an appropriate selector switch being provided to permit selection of a particular desired endpoint without re' calibration. Additionally, multiple endpoint titrations can be carried out by using multiple indicators and a separate logarithmic ratiometer, meter relay, clock, and separate pairs of filters and light detectors for each indicator.

What is claimed is:

1. Apparatus for determining bicarbonate ion in a test sample, comprising means for containing a measured test sample which has been acidified with a predetermined quantity of acid to provide a liquid mixture; means for flushing out dissolved carbon dioxide generated by the acidification of said sample; means for coulometrically titrating said acidified flushed sample by passing an electrolysis current through said acidified test sample between an anode and a cathode disposed in the liquid at which hydroxyl ions are generated in said liquid mixture to titrate the acidity of said mixture; a pH indicator in the sample having acid and base forms of different color and adapted to change between the acid and base forms over a pH range which includes the acid-base endpoint of the titration; means for directing light through the said acid mixture, and for providing first and second beams of light colorimetrically responsive to the concentrations of the acid and base forms, respectively, of the indicator in the liquid; photoelectric light detecting means for providing first and second signals corresponding to the intensity of the first and second beams of light; means for providing a third signal corresponding to the ratio of the logarithms of the first two signals, means for detecting when the third signal reaches a predetermined value corresponding to the acid-base endpoint; means for measuring the quantity of electricity carried during said electrolysis until said acid-base endpoint is reached; and connecting means between said detecting means and said means for measuring the quantity of electricity for signalling to the measuring means that said acid-base endpoint has been reached.

2. In a device for automatic titration of a liquid containing an indicator substance adapted to change between different forms having different light absorption characteristics over a color change interval indicative of a predetermined endpoint, said device comprising means for introducing titrant ions into a liquid to be titrated, means for detecting the endpoint, means for measuring the amount of titrant ions required to achieve the endpoint, the improvement wherein the means for detecting the endpoint comprises:

means for directing light through the liquid;

means for providing first and second light beams, the

intensity of each light beam being colorimetrically responsive to one form of the indicator;

light detecting means for generating first and second signals corresponding to the intensities of the first and second light beams;

means for generating a third signal corresponding to the ratio of the logarithms of the first and second signals;

means responsive to the third signal generating means for detecting when the third signal reaches a predetermined value corresponding to the endpoint; and

means responsive to said third signal detecting means for signalling to the measuring means that the endpoint has been reached.

3. The device of claim 2 wherein the means for supplying the titrant ions includes a constant current source for electrolytically generating titrant ions in the liquid, wherein the titrant measuring means includes a timer connected to the current source, and wherein the means for signalling that the endpoint has been reached includes means for deactivating the timer and the constant current source.

4. The device of claim 2 wherein the means for generating the third signal comprises logarithmic amplifier means connected to the light detector means for providing outputs proportional to the logarithms of the first and second signals, and ratiometer means connected to the logarithmic amplifier means for providing an output signal proportional to the ratio of the logarithms of the first and second signals.

5. The device of claim 4 wherein the liquid to be titrated is an acidic solution of an acid-base indicator, wherein the means for supplying the titrant ions includes means for passing an electrolysis current through the liquid to generate hydroxyl ions therein, and wherein the measuring means comprises means for measuring the quantity of electricity carried by said titrant ion supplying means.

6. A method useful for colorimetric titration of a liquid having different light absorption characteristics on different sides of a color change interval indicative of a predetermined endpoint, comprising:

introducing a titrant into the liquid;

passing light through the liquid during the introduction of titrant;

generating a first electrical signal corresponding to the intensity of light passed through the liquid at a first wave length corresponding to the light absorption characteristics of the liquid at one side of the color change interval; generating a second electrical signal corresponding to the intensity of the light passed through the liquid at'a second wavelength corresponding to the light absorption characteristics of the liquid at the other side of the color change interval;

generating a third electrical signal corresponding to the ratio of the logarithms of the first and second signals;

continuing the introduction of titrant until the third signal reaches a predetermined value corresponding to said endpoint; and

measuring the quantity of titrant introduced into said liquid prior to the time said third signal reaches said predetermined value.

7. The method of claim 6 wherein the third signal is generated by generating signals corresponding to the logarithms of the first and second signals, and generating a ratio signal corresponding to the ratio of the logarithmic signals.

8. A method useful for colorimetric titration of a liquid acidic solution of an acid-base indicator having different light absorption characteristics on different sides of a color change interval indicative of predetermined acid-base endpoint, comprising:

passing an electrolysis current through said liquid to generate hydroxyl ions therein to titrate the acidiy;

passing light through the liquid during the titration thereof;

the liquid in said electrolysis current until the ratio of said logarithms reaches the predetermined value corresponding to the endpoint.

9. The method of claim 8 wherein the liquid to be titrated is prepared by mixing together serum containing an unknown amount of bicarbonate ion, bicarbonate-free acid in excess of an amount required to neutralize the bicarbonate ion in the serum, and an acid-base indicator which changes from an acid form to a base form over a pH range which includes a pH value of 7.4. 

2. In a device for automatic titration of a liquid containing an indicator substance adapted to change between different forms having different light absorption characteristics over a color change interval indicative of a predetermined endpoint, said device comprising means for introducing titrant ions into a liquid to be titrated, means for detecting the endpoint, means for measuring the amount of titrant ions required to achieve the endpoint, the improvement wherein the means for detecting the endpoint comprises: means for directing light through the liquid; means for providing first and second light beams, the intensity of each light beam being colorimetrically responsive to one form of the indicator; light detecting means for generating first and second signals corresponding to the intensities of the first and second light beams; means for generating a third signal corresponding to the ratio of the logarithms of the first and second signals; means responsive to the third signal generating means for detecting when the third signal reaches a predetermined value corresponding to the endpoint; and means responsive to said third signal detecting means for signalling to the measuring means that the endpoint has been reached.
 3. The device of claim 2 wherein the means for supplying the titrant ions includes a constant current source for electrolytically generating titrant ions in the liquid, wherein the titrant measuring means includes a timer connected to the current source, and wherein the means for signalling that the endpoint has been reached includes means for deactivating the timer and the constant current source.
 4. The device of claim 2 wherein the means for generating the third signal comprises logarithmic amplifier means connected to the light detector means for providing outputs proportional to the logarithms of the first and second signals, and ratiometer means connected to the logarithmic amplifier means for providing an output signal proportional to the ratio of the logarithms of the first and second signals.
 5. The device of claim 4 wherein the liquid to be titrated is an acidic solution of an acid-base indicator, wherein the means for supplying the titrant ions includes means for passing an electrolysis current through the liquid to generate hydroxyl ions therein, and wherein the measuring means comprises means for measuring the quantity of electricity carried by said titrant ion supplying means.
 6. A method useful for colorimetric titration of a liquid having different light absorption characteristics on different sides of a color change interval indicative of a predetermined endpoint, comprising: introducing a titrant into the liquid; passing light through the liquid during the introduction of titrant; generating a first electrical signal corresponding to the intensity of light passed through the liquid at a first wave length corresponding to the light absorption characteristics of the liquid at one side of the color change interval; generating a second electrical signal corresponding to the intensity of the light passed through the liquid at a second wavelength corresponding to the light absorption characteristics of the liquid at the other side of the color change interval; generating a third electrical signal corresponding to the ratio of the logarithms of the first and second signals; continuing the introduction of titrant until the third signal reaches a predetermined value corresponding to said endpoint; and measuring the quantity of titrant introduced into said liquid prior to the time said third signal reaches said predetermined value.
 7. The method of claim 6 wherein the third signal is generated by generating signals corresponding to the logarithms of the first and second signals, and generating a rAtio signal corresponding to the ratio of the logarithmic signals.
 8. A method useful for colorimetric titration of a liquid acidic solution of an acid-base indicator having different light absorption characteristics on different sides of a color change interval indicative of predetermined acid-base endpoint, comprising: passing an electrolysis current through said liquid to generate hydroxyl ions therein to titrate the acidity; passing light through the liquid during the titration thereof; measuring the intensity of light passed through the liquid at a first wavelength corresponding to the light absorption characteristics of the liquid at one side of the color change interval; measuring the intensity of the light passed through the liquid at a second wavelength corresponding to the light absorption characteristics of the liquid at the other side of the color change interval; continuing the titration until the ratio of the logarithms of the intensities of said light at the first and second wavelengths reaches a predetermined value corresponding to said endpoint; and measuring the amount of electricity passed through the liquid in said electrolysis current until the ratio of said logarithms reaches the predetermined value corresponding to the endpoint.
 9. The method of claim 8 wherein the liquid to be titrated is prepared by mixing together serum containing an unknown amount of bicarbonate ion, bicarbonate-free acid in excess of an amount required to neutralize the bicarbonate ion in the serum, and an acid-base indicator which changes from an acid form to a base form over a pH range which includes a pH value of 7.4. 